Scattering length bound-atom

The scattering lengths discussed so far refer to a fixed nucleus. If the nucleus is free to vibrate, it will recoil under the impact of the neutron. In that case the effective mass is that of the compound nucleus, consisting of the neutron and the scattering nucleus. This means that the neutron mass m must be replaced by the reduced mass of the compound nucleus (i = mM/(M + m), where M is the mass of the scattering atom. As a result, the scattering length of the free atom is related to that of the bound atom by... 

Table 2 Bound scattering lengths, i>(fm) and cross section for selected isotopes and for selected naturally occurring isotopic mixtures of the elements u(hams, 1 bam = 100 fm ). Z, atomic number A, mass number I, spin of the nuclear groimd state i>coh> bine, coherent and incoherent scattering lengths ffa, ffeCh, coherent and incoherent cross sections ffa, absorption cross section for 2.2 km s neutrons ...

Consider first of all the scattering of neutrons by the nuclei in a monoatomic liquid. This process is characterized by a scattering cross-section, Qq, which, in turn, is related to Z>d, the bound atom scattering length. For slow neutrons. 

It is interesting to note that the value of the scattering length a for atoms A can be obtained from laser spectroscopy by measuring the energy and the vibrational wave function of the last bound vibrational level in the ground-state potential of the molecule A2 [1194],... 

TABLE 23.1. Bound atom scattering lengths and cross sections for typical elements in synthetic and natural polymers. 

In decays of heavy unstable particles many charged mesons can be emitted simultaneously. If two of them are oppositely charged and have close trajectories, they can form a bound state. Nemenov (2000) quotes the experimental study of tt p, Jt jt , and Jt K atoms from which scattering lengths were deduced for the two-particle systems involved. 

Figure 6.6 shows an example of the scattering length and bound-state energies for the molecule near the lowest energy spin channel of the separated atoms. The... 

The s-wave scattering of two Rb atoms on theX E+ potential at the energies of interest is influenced by a resonance enhancing the scattering length to above 2400 au [85,86]. The resonance arises from the last (quasi-) bound state lying very close to the continuum threshold [90], Hence, the amplitude of the continuum wavefunction in the inner region is enhanced relative to the nonresonant case. This enhances the Franck-Condon factors for theX S+ — — b Yl continuum-bound transitions in Rb2. 

Most ongoing experiments with Fermi gases of atoms in two different internal (hyperfine) states use wide Feshbach resonances [52], For example, weakly bound molecules Li2 and have been produced in experiments [10-20] by using Feshbach resonances with a length R < 20 A, and for the achieved values of the scattering length a (from 500 to 2000 A) the ratio R /a was smaller than 0.1. In this review we will consider the case of a wide Feshbach resonance. 

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